The Dow Jones Industrial Average rose more than 25 points, led by Chevron, Hewlett-Packard, and Cisco , while Home Depotand American Express declined.

The S&P 500 gained slightly while the tech-heavy Nasdaq slipped. The CBOE Volatility Index, widely considered the best gauge of fear in the market, fell to about 17.6.

Most key S&P sectors rose, led by energy, materials and utilities. The consumer discretionary sector, which has risen sharply in recent months, fell.

Volume on the consolidated tape of the New York Stock Exchange was trending slightly higher than Monday's record low levels. On Monday, 2.6 billion shares changed hands, a little more than half the average daily volume, and the lowest level for a full day of trading since Dec. 31, 2009. As of 3:30 p.m. Tuesday 1.7 billion shares changed hands.

Despite the light, lackluster trading, the markets largely continued to trend higher. As of Monday, the Dow has risen 5 percent for December and nearly 11 percent for the year-to-date. The S&P 500 has risen 6.5 percent for the month, and 12.7 percent for the year-to-date. The Nasdaq rose 6.7 percent for December, and 17.5 percent for the year-to-date.

Some market market participants expect the good news to continue.

"On a short term basis, we like the market and think it will continue its upward surge," Yu-Dee Chang, chief principal at ACE Investment Strategists, a money management firm, told CNBC.com.

Chang expects the market will perform similar in 2011 to how it performed in 2010, surging upward, then pulling back.

"There will be an upward bias, but it won’t be smooth," he said. Specifically, Chang sees the markets pulling back every two months within a range of 4 percent to 17 percent. "If we get surprises in economic numbers, that will initiate a pull back," Chang said.

His strategy for now is to focus on networking companies like Cisco that should do well as the economy improves and businesses seek to upgrade equipment, as well as stocks of emerging economies in China and India, as well as gold, which Chang said should continue to appreciate.

He also likes consumer discretionary stocks even though the sector has surged more than 26 percent so far this year. But investors who haven't bought the sector so far should be cautious, he said.

James Paulsen, chief investment strategist at Wells Capital Management, agrees the market will continue to rise, and predicts another double-digit returnfor next year, but like Chang, Paulsen told CNBC investors shouldn't expect the markets to experience a straight run-up in 2011. Instead, expect the pattern to “ebb and flow,” he said.

Oil prices rose slightly to close shy of a 26-month high $91.88 a barrel, aided in part by a weaker dollar , which fell against a basket of currencies on Tuesday.

Gold jumped 1.7 percent to close at $1,405 an ounce,while copper futures hit a new high.

Just over a month after its initial public offering, General Motors was lavished with positive ratingsby Wall Street brokerages, sending its shares higher, as the automaker heads into a new product cycle.

GM was initiated at a "buy" rating by Citigroup and Bank of America Merrill Lynch, at "outperform" by RBC Capital and Credit Suisse, and at "overweight" by Morgan Stanley, JPMorgan, and Barclays Capital. Price targets for GM ranged from $42 a share at Barclays and RBC Capital, to $50 share at Morgan Stanley. Soleil Securities was the only brokerage with a cautious forecast, initiating the stock at a "hold" and a price target of $38 a share.

In tech news, Hewlett-Packard shares rose after news the tech giant won a $2.5 billion 10-year contract to provide computers and services to NASA.

And Apple advanced after a report in The Telegraph that it has received a patent that will allow it to create a screen that produces 3D and holographic images.

A survey by the International Council of Shopping Centers and Goldman Sachs found chain store sales in the week ended Dec. 25rose 4.8 percent from the same period a year earlier, the best gain since April, and putting retail sales on track to rise 4 percent in November and December.

Meanwhile, Sears rose after news the retailer launched an online movie download service, Alphaline Entertainment. Sears and K-Mart customers can use the service to download movies the same day they are released on DVD.

Molycorp sharesslumped after soaring more than 8 percentafter news the rare earth metals miner would be ready to extract metals from its mine in Mountain Pass, California, for another year. The company's shares had spiked following China's announcement that it was curtail its rare-earth metals exports, a move that would benefit the U.S. producer.

Metals and mining stocks rebounded, including Newmont Mining and Barrick Gold , after dipping on Monday in the wake of China's interest-rate hikes.

AIG could net up to $3 billion as it tries again to sell its Taiwan insurance unit. (Video: Should you buy AIG shares, which is up almost 100% this year?)

Treasury prices fell after the government auctioned $35 billion of 5-year notes to a weak reception. The new five-year notes yielded 2.149 percent and had a bid-to-cover ratio of 2.61. Prices throughout the bond market fell after the auction and head of the government's auction of $29 billion in seven-year notes on Wednesday. The 10-year note dropped a point in price to yield 3.47 percent.

In economic news, the Conference Board's index of consumer confidence fell to 52.5 in December from a revised 54.3 in November, and less than the reading of 56 expected by economists surveyed by Reuters. The index showed consumers remain concerned about the weak job market.

The Standard & Poor's/Case-Shiller price index fell in October from September, as home prices continued to fall broadly.

Homebuilders including D.R. Horton , KBHome and Pulte declined.

“The double-dip is almost here, as six cities set new lows for the period since the 2006 peaks," David Blitzer, chairman of the index committee at S&P, said in a statement. "There is no good news in October’s report. Home prices across the country continue to fall.”

In other news, President Obama is expected to announce his choice for the White House's top economic advisor on his return from the holiday break.

European shares were mostly higher with health care and technology stocks leading the gains. Volumes were also light with the U.K. market closed for a public holiday. The French market was higher despite the country's gross domestic product growth for the second and third quarter being revised down slightly.